C&O Seminar - James Renegar

Title: A framework for applying subgradient methods to conic optimization
problems

Abstract: A framework is presented whereby a general convex conic
optimization problem is transformed into an equivalent convex
optimization problem whose only constraints are linear equations (one
more equation than the original problem), and whose objective function is
Lipschitz continuous.  Virtually any subgradient method can be applied to
solve the equivalent problem.  Two methods are analyzed.

Moreover, we show that for a broad class of optimization problems
(namely, hyperbolic programs), the equivalent problems can be naturally
"smoothed," thus allowing accelerated gradient methods to be applied,
resulting in superior iteration bounds.

Perhaps most surprising is that the transformation is simple and so is
the basic theory, and yet the approach has been overlooked until now, a
blind spot.